All subjects with the study will be children (age 6-12) with Attention Deficit Hyperactivity Disorder (ADHD). After baseline assessment confirms the presence of ADHD, children will have an Event related potential (ERP) (a type of electroencephalogram [EEG]) study. After the baseline EEG, children will be randomized to either placebo or GXR for a 4-week, parallel groups trial. During this trial, dosing will be flexibly adjusted according to patient response or presence of side effects. The dosage will range from 1-4 mg. At the end of the four week trial, a follow up ERP study will be obtained.